2.619   ODE No. 619

$y'(x)=\frac {6 y(x)}{-F\left (-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)+x\right )+8 y(x)^4+9 y(x)^3+12 y(x)^2+6 y(x)}$ Mathematica : cpu = 0.674247 (sec), leaf count = 330

$\text {Solve}\left [\int _1^{y(x)}\left (-\frac {8 K[2]^3}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {9 K[2]^2}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {12 K[2]}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}-\frac {F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right ) \int _1^x-\frac {6 \left (-\frac {4}{3} K[2]^3-\frac {3 K[2]^2}{2}-2 K[2]-1\right ) F'\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+K[1]\right )^2}dK[1]+6}{F\left (-\frac {1}{3} K[2]^4-\frac {K[2]^3}{2}-K[2]^2-K[2]+x\right )}+\frac {1}{K[2]}\right )dK[2]+\int _1^x\frac {6}{F\left (-\frac {1}{3} y(x)^4-\frac {y(x)^3}{2}-y(x)^2-y(x)+K[1]\right )}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.532 (sec), leaf count = 81

$\left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{\it \_a}} \left ( -8\,{{\it \_a}}^{4}-9\,{{\it \_a}}^{3}-12\,{{\it \_a}}^{2}+F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{\it \_a}}^{2}-{\it \_a}+x \right ) -6\,{\it \_a} \right ) \left ( F \left ( -{\frac {{{\it \_a}}^{4}}{3}}-{\frac {{{\it \_a}}^{3}}{2}}-{{\it \_a}}^{2}-{\it \_a}+x \right ) \right ) ^{-1}}\,{\rm d}{\it \_a}-{\it \_C1}=0 \right \}$